1. Field of the Invention
The present invention relates generally to communications signal handling methods and apparatus and more particularly to a complex ternary correlator method and apparatus for use in developing the tap coefficient update increments in an adaptive equalizer.
2. Description of the Prior Art
A typical prior art communication system adaptive equalizer is illustrated generally at 10 in FIG. 1 and has as its functional objective the restoration of channel distorted data x(t) to a very close approximation y(t) of the originally transmitted data z(t) which is then input to a detector 16. FIG. 1 illustrates a decision feedback equalizer, but similar correlation and gradient computation is required for feedforward or hybrid feedforward/feedback equalizers. The feedback equalizer is comprised of three principal components: a transversal filter portion 14 which linearly processes prior detected symbols z(t); a gradient computation portion 18 which adjusts the tap coefficients 24 of the transversal filter; and a detector (or decision) portion 16 which identifies an input signal as one of a predetermined set of signals. An example of one such detector is the V.29 constellation detector disclosed in the copending application of Bruce M. Sifford, Ser. No. 960,851, filed Nov. 15, 1978.
Adaptive equalizers of the type illustrated at 10 in FIG. 1 of the drawing have their tap coefficients 24 adaptively adjusted on the basis of the pseudo-error signal e(t) which is generated by subtracting the equalized data y(t) from the complex data output z(t). Ideally, this error signal would be generated by comparing the equalizer output y(t) with the true data z(t). However, for practical communication systems this is impossible, and the pseudo-error signal e(t) is formed using the data detector output z(t) instead of z(t). Under normal circumstances this is acceptable since z(t) and z(t) almost always agree.
The decision feedback equalizer of a typical receiver system exploits the fact that at the output of the communication channel 12 there is residual intersymbol interference from previous symbols transmitted. Assuming that correct decisions have already been made on these past symbols, the late-arriving contributions can then be subtracted from the current-received signal x(t). The mechanism for accomplishing this is to excite a complex tapped-delay-line filter with the complex decision signals that have been made and then subtract the weighted filter tap outputs from the incoming complex signal. The taps are continuously adjusted to minimize the average error signal e(t) produced at the receiver output.
The tap coefficients may be updated at each sampling instant, and each new tap coefficient is the old value plus a new increment (which might be 0); that is, EQU a.sub.i (t+1)=a.sub.i (t)+.DELTA.a.sub.i (t+1) (1)
for i=1 to n where n is the number of taps.
The increment is calculated on the basis of the adaptive gradient algorithm EQU a(t+1)=a(t)+k.multidot.e(t).multidot.z*(t-1) (2)
where
a(t), e(t) and z(t) are complex-valued functions,
e(t) is the complex pseudo-error signal,
z(t) is the complex detector output,
k is a scaling factor, and
the * denotes complex conjugate.
It may thus be shown that the gradient is proportional to the cross correlation between the pseudo-error and the detector output data, i.e., e(t)z(t-i), where the superbar denotes an averaging process that is performed by the above equation (1). The new increment, .DELTA.a.sub.i, is then based directly on this cross correlation. This approach is generally referred to as an analog correlator method even though in this disclosure it is implemented in an integer, fixed-word-length realization.
The disadvantage of this "analog" correlator method is that it requires one p-bit (typically p=8) multiplier for each of the n taps of the transversal filter. Since n is frequently greater than 16, and may be as high as 64, this is a very costly requirement. The purpose of this invention is to substantially reduce the complexity of these correlators.